Pulse compression radar systems utilize waveforms that have narrow autocorrelation functions and time-bandwidth products that are much higher than unity enabling good range resolution (bandwidth dependent) and target detection (energy dependent). In operation, a known electromagnetic pulse is transmitted from a transmitting device, e.g., a transmitter or transceiver, and the transmitted pulse reflects off an object. The reflected signal is received at the receiver or transceiver and undergoes various signal processing techniques including signal pulse compression. For example, the received reflected signal is pulse-compressed by correlating the received reflected signal against a replica of the transmitted signal. The graphical result of a cross-correlation is illustrated in FIG. 1, which shows a composite function including a mainlobe 10 and a plurality of sidelobes 20. In contrast to the composite function illustrated in FIG. 1, an ideal autocorrelation function will have a mainlobe width of zero and zero sidelobes. However, practical finite-duration and finite-bandwidth waveforms have non-zero autocorrelation widths and finite sidelobe levels, which limit the target dynamic range. The limited dynamic range may have a negative effect on the radar system as a weaker target may be located in one of sidelobes and therefore avoid being detected.
Various methodologies have been proposed to reduce the sidelobe levels. For example, one such method includes multiplying the signal after pulse compression by an amplitude function that is maximized at the center and approaches zero at the edges. Such a method is referred to as “apodization”. U.S. Pat. No. 5,349,359 issued to Dallaire et al., the entirety of which is incorporated by reference herein, discloses a method of spatially variant apodization (SVA). SVA is a type of nonlinear filter that suppresses unwanted sidelobes and preserves the mainlobe.
As taught by Dallaire, the method of applying an SVA filter to a signal includes determining the weights for each sample, n, of the received signal. The weights are calculated according to the following expression:
                    w        =                              -                          [                                                I                  i                  2                                +                                  Q                  i                  2                                            ]                                            [                                                            I                  i                                ⁡                                  (                                                            I                                              i                        -                        1                                                              +                                          I                                              i                        +                        1                                                                              )                                            +                                                Q                  i                                ⁡                                  (                                                            Q                                              i                        -                        1                                                              +                                          Q                                              i                        +                        1                                                                              )                                                      ]                                              Eq        .                                  ⁢        1            Where,
Ii represents the real component of the current sample;
Qi represents the imaginary component of the current sample;
Ii−1 represents the real component of the previous sample;
Qi−1 represents the imaginary component of the previous sample;
Ii+1 represents the real component of the following sample; and
Qi+1 represents the imaginary component of the following sample.
The output of the SVA filter, y(n), is based on the input of the SVA filter, x(n), and the weight, w, of the current sample as calculated in accordance with Equation 1 as follows:
                                          y            ⁡                          (              n              )                                =                      x            ⁡                          (              n              )                                      ;                            w        <        0                                                      y            ⁡                          (              n              )                                =                                    x              ⁡                              (                n                )                                      ⁡                          [                              1                -                                  0.5                  w                                            ]                                      ;                            w        >        0.5                                                      y            ⁡                          (              n              )                                =          0                ;                            0        ≤        w        ≤        0.5            
The SVA filter can be difficult to implement in hardware because of discontinuities in filter outputs when the calculated weight of the sample is greater than or equal to zero and less than or equal to one-half. In addition, the SVA filter may not be implemented for all waveforms types including, for example, non-linear frequency modulated (NLFM) waveforms. NLFM waveforms have lower peak sidelobe levels (PSLs) and do not incur losses due to weighting compared to linear frequency modulated (LFM) waveforms. Additionally, NLFM waveforms have a constant-amplitude envelope, which enables efficient generation of high power signals, with a continuous phase so that they are spectrally well contained. Accordingly, these features have led to the implementation of NLFM waveforms in pulse compression radar systems for tracking targets.
Accordingly, an improved SVA filter design that is suitable for use with NLFM waveforms is desirable.